How to write the combination formula $x \choose y $ for 3 numbers? This is my problem:

We have a die with these sides (1,1,1,1,2,3), all sides are equiprobable. We are rolling 10 times. What is the probability of having 6*1, 3*2 and 1*3?



You can use the multinomial coefficient.

$\displaystyle{n \choose k_1, k_2, \ldots, k_m} = \frac{n!}{k_1!\, k_2! \cdots k_m!}$

In your case it is $m=3, k_1=6,k_2=3, k_3=1$

$\displaystyle{10 \choose 6, 3, 1}$


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